AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
− A = not A A ∙ B = A and B A + B = A or B Identification and use of AND,…
Full specification wording
Combinational logic (A-level only): − A = not A A ∙ B = A and B A + B = A or B Identification and use of AND, NAND, OR, NOR, NOT and EOR gates in combination in logic circuits.
This statement fixes the notation and the gate set.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 2 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
This statement fixes the notation and the gate set. A bar over a variable means NOT, so A̅ is the inverse of A. A dot means AND, so A ∙ B is 1 only when both inputs are 1. A plus means OR, so A + B is 1 when at least one input is 1. The gates to know are AND, NAND (an AND followed by NOT), OR, NOR (an OR followed by NOT), NOT and EOR (exclusive-OR, 1 when inputs differ). In combination, gates form circuits whose overall behaviour you find by working through each gate in turn, then checking against a truth table.
For example: A NAND B followed by a NOT gate returns A AND B.
What earns the marks
- Interpret the symbols: a bar denotes NOT, a dot denotes AND and a plus sign denotes OR.
- State the output of each gate: AND gives 1 only for 1,1; OR gives 1 for any 1; NOT inverts; NAND and NOR invert AND and OR outputs; EOR gives 1 when inputs differ.
- Analyse a multi-gate circuit by labelling the output of each gate and combining them stage by stage.
- Construct a truth table for a combined circuit and use it to identify the overall logic function.
- Select and combine gates to realise a required Boolean expression or truth table.
- Recognise that NAND and NOR are inverted forms of AND and OR, and that EOR differs from OR only for the 1,1 input.
Common mistakes and how to put them right
Treating EOR as identical to OR; OR gives 1 for 1,1 but EOR gives 0, so the two differ on that row.
Forgetting that NAND and NOR invert the whole AND or OR result, not just one input.
Reading a bar as covering only the nearest variable when it spans a whole expression.
Put it right: A bar over A + B means NOT(A OR B), not (NOT A) OR B.
Exam tips
- Annotate intermediate gate outputs on the diagram before writing the final expression.
- Build the truth table column by column, one gate at a time, so errors are easy to spot.
- For a required function, start from its truth table and choose gates that produce 1 on exactly the needed rows.
Try the lesson
The start of the Combinational logic (A-level only): − A = not A A ∙ B = A and B A + B = A or B Identification and use of AND, NAND, OR, NOR, NOT and EOR gates in combination in logic circuits. lesson, made from checked teaching notes for this specification point.
Have a go first
In Boolean algebra, which expression represents the output of a NOT gate applied to input A?
Listen
This statement fixes the notation and the gate set. A bar over a variable means NOT, so A̅ is the inverse of A. A dot means AND, so A ∙ B is 1 only when both inputs are 1. A plus means OR, so A + B is 1 when at least one input is 1. The gates to know are AND, NAND (an AND followed by NOT), OR, NOR (an OR followed by NOT), NOT and EOR (exclusive-OR, 1 when inputs differ). In combination, gates form circuits whose overall behaviour you find by working through each gate in turn, then checking against a truth table. For example, A NAND B followed by a NOT gate returns A AND B. A strong answer earns marks for these points. Interpret the symbols: a bar denotes NOT, a dot denotes AND and a plus sign denotes OR. State the output of each gate: AND gives 1 only for 1,1; OR gives 1 for any 1; NOT inverts; NAND and NOR invert AND and OR outputs; EOR gives 1 when inputs differ. Analyse a multi-gate circuit by labelling the output of each gate and combining them stage by stage. Construct a truth table for a combined circuit and use it to identify the overall logic function. Exam tip: Annotate intermediate gate outputs on the diagram before writing the final expression.
Key words
Say what each word means before you turn the card.
NOT
Try answering aloud or in your head before turning the card.
AND
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OR
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EOR
Try answering aloud or in your head before turning the card.
See every definition
- NOT
- A bar over a variable means NOT, so the output is the inverse of the input.
- AND
- A dot means AND, so the output is 1 only when both inputs are 1.
- OR
- A plus means OR, so the output is 1 when at least one input is 1.
- EOR
- Exclusive-OR gives 1 when inputs differ, and differs from OR only for the 1,1 input.
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